A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following with not be affected ?

Options

A. moment of inertia
B. angular velocity
C. angular momentum
D. rotational kinetic energy

Explanation

To solve the problem, we need to analyze how various physical quantities related to a solid sphere change when its radius is increased while keeping its mass constant.

### Step-by-Step Solution:

1. **Understand the Definitions**:
- **Moment of Inertia (I)**: For a solid sphere, the moment of inertia is given by the formula:
\[ I = \frac{2}{5} m r^2 \]
where \( m \) is the mass and \( r \) is the radius of the sphere.

2. **Effect of Increasing Radius**:
- If the radius \( r \) is increased while keeping the mass \( m \) constant, the moment of inertia \( I \) will increase because it is directly proportional to the square of the radius.

3. **Angular Momentum (L)**:
- Angular momentum \( L \) is given by:
\[ L = I \omega \]
where \( \omega \) is the angular velocity. Since the sphere is rotating in free space, and there are no external torques acting on it, angular momentum must be conserved.

4. **Conservation of Angular Momentum**:
- As the moment of inertia \( I \) increases due to the increase in radius, the angular velocity \( \omega \) must decrease to keep \( L \) constant. Therefore, if the radius increases, the angular velocity will decrease.

5. **Rotational Kinetic Energy (K)**:
- The rotational kinetic energy is given by:
\[ K = \frac{1}{2} I \omega^2 \]
Since \( I \) increases and \( \omega \) decreases (and specifically, it decreases in such a way that \( L \) remains constant), the overall effect is that the rotational kinetic energy will decrease.

6. **Conclusion**:
- The quantities that will be affected are:
- Moment of Inertia (will increase)
- Angular Velocity (will decrease)
- Rotational Kinetic Energy (will decrease)
- The quantity that will **not be affected** is the **Angular Momentum**, which remains constant.

### Final Answer:
The quantity that will not be affected is **Angular Momentum**.